• IE interfaces
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• v.23 no.4
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• pp.337-348
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• 2010

The Bass model is the most widely used model in research of new product diffusion because it presents a nice explanation on the diffusion process of new products. However, it has a limitation that its performance of fitness is lower as the available data become less and also, the diffusion curve is bell-shape and so, it can not represent the various diffusion patterns. Recently, a two-pieces Bass model is developed and applied to analyze diffusion of 10 products. The results are encouraging in terms of fitness. However, diffusion pattern is not dealt with in the paper. In this paper, analysis of diffusion pattern is in depth addressed in two-pieces Bass model. It is shown that the diffusion curves are divided into 3 types with respect to the peak adoption rate and each type is divided into 2 types further. Takeoff time of a diffusion process is analyzed by using the inflection point and regime-change time where it represents the point that imitation and innovation parameters change. Empirical studies for 68 products(28 domestic products and 40 USA products) are performed to analyze the diffusion pattern. Findings are that diffusion patterns of all products except 1 USA product show type I and regime-change time becomes shorter as the introduction time of the product is later in domestic products and regime-change time can be regarded as a takeoff time in 47% of total 68 products.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.9
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• pp.108-115
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• 2018

Time is considered as an important factor to understand the diffusion behavior of single generation technology. However, multiple generation technology required additional factors in addition to time to understand the diffusion behavior. This study defined the diffusion path of multiple generation technology based on dimensions of 'time, price, and performance' after extracting price and technical performance factors and traced the diffusion path of semiconductor industry based on defined dimensions. The case study of semiconductor industry indicated that the diffusion path is determined maximizing the integrated area of price and performance. This study has theoretical implications in that it analyzed the diffusion behavior of multiple generation technology based on multiple dimensions and can forecast the diffusion behavior at matured as well as early stage technology. Also, this study has practical implications for R&D and marketing managers to understand time-to-market, exit time, and economical as well as technical requirements.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.443-459
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• 2006

The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\;{\leq}\;{\infty}$. By obtaining the bounds of $W\array_2^1$-norms of the local solution independent of T we establish the global existence of the solution. And the long-time behaviors of the global solution are analyzed when the diffusion rates $d_1\;and\;d_2$ are sufficiently large.

• Journal of the Korea Concrete Institute
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• v.21 no.3
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• pp.377-386
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• 2009

A reference diffusion coefficient model from ACI life-365 is drawn from test results by NT build 443. This test method gives a time-averaged diffusion coefficient during immersion period, thus the ACI model uses the time-averaged diffusion coefficient as a reference value. ACI model needs to be revised, considering the difference between the time-average value and reference value at specified time. In this study, firstly the analytic solutions of diffusion equation are derived considering the initiation time and period of exposure to chloride, and secondly the time-averaged diffusion coefficient from NT build 443 is converted into the diffusion coefficient at reference time. From this study, the reference diffusion coefficient of ACI model should be modified to be about 10% larger values than those of present ACI model. For convenient design of service life, previous relationship between the chloride diffusion coefficient from NT build 443 and that from NT build 492 is also modified. To compare the chloride diffusion coefficients of ACI and JCI models, the reference chloride diffusion coefficient with respect to the JCI model is drawn in the similar form of ACI model's, and service life prediction by ACI life-365 method is confirmed to give a conservative result.

• Journal of Korea Planning Association
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• v.53 no.7
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• pp.23-37
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• 2018

In recent years, there has been a proliferation of commercial uses in the area where Gentrification occurs. In order to cope with such a diffusion phenomenon, it is necessary to derive the diffusion area accurately. Gentrification has a feature that occurs locally in a short time. Therefore, this study used the space-time pattern analysis to derive the diffusion area of commercial uses in Bukchon, a typical gentrified area in Seoul. Among the space-time pattern analysis, space time permutation statistics used in this study can derive the convergence phenomenon of time and space in a particular case with only the location information. The results confirmed that there has been three proliferation area in Bukchon, one started in 2007, other in 2013 and the other in 2014. In the earliest area, independent shops were the most popular, and the majority of them were restaurants. However in latter areas, there has been more chain stores and clothing stores than earlier area. The findings of this study indicate that space time pattern analysis can be used as a tool to analyze the proliferation by gentrification because it can derive accurate location and timing of the diffusion.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• Journal of Welding and Joining
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• v.9 no.3
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• pp.26-33
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• 1991

As it takes very long time for the Transient Liquid Phase(TLP) bonding, we tried to reduce the bonding time by changing insert material for the high diffusivity element. On this study boron powder was doped as a insert material on the bonding surface of Rene 80 superalloy, and diffusion treated at 1150.deg.C under vacuum. On this method differently from the TLP bonding the insert material was not melted during bonding but only the base metal reacted with the boron was inducedly melted. Therefore, as this bonding mechanism is different from the existing ones, it is suggested as a Melting Induced Diffusion Bonding. When this process was used for the diffusion bonding, the bonding time including homogenization decreased greatly compared to the conventional TLP bonding.

• Bulletin of the Korean Chemical Society
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• v.26 no.11
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• pp.1723-1727
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• 2005

A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as $\psi(t) \sim (t) ^{-(\alpha+1)}$, the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < $r^2(t)$ > ~ $t ^{2\alpha/dw}$, where $d_w$ is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.4
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• pp.494-502
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• 1997

Experiments on corresponding jet flames with stagnant point diffusion flames have been carried out in initial injection periods. A compensated measurement of maximum flame temperature, which is based on the ion signal, has been employed to inspect flame responses to time-varying strain rates. The flame responses are obtained at two conditions for the slowly time-varying strain rate and the case of flame extinction, and analyzed to confirm similarity between a stagnant point diffusion flame and an evolving jet diffusion flame. Nonsteady effects are addressed via the comparison between several time scales. The time variation with low strain rates, in which illustrates the flame behavior of the upper branch far from extinction in the well-known S-curve, is confirmed to produce a quasi-steady flame response through the nonsteady experiments. The time variation with strain rates in the case of flame extinction indicates an unsteady effect of flame response. It is therefore found that the flame responses near jet tip depend on time histories of characterized strain rates in the developing process.

• Geophysics and Geophysical Exploration
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• v.17 no.3
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• pp.129-136
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• 2014

Electromagnetic (EM) methods are generally divided into frequency-domain EM (FDEM) and time-domain EM (TDEM) methods, depending on the source waveform. The FDEM and TDEM fields are mathematically related by the Fourier transformation, and the TDEM field can thus be obtained as the Fourier transformation of FDEM data. For modeling in time-domain, we can use fast frequency-domain modeling codes and then convert the results to the time domain with a suitable numerical method. Thus, frequency-to-time transformations are of interest to EM methods, which is generally attained through fast Fourier transform. However, faster frequency-to-time transformation is required for the 3D inversion of TDEM data or for the processing of vast air-borne TDEM data. The diffusion expansion method (DEM) is one of smart frequency-to-time transformation methods. In DEM, the EM field is expanded into a sequence of diffusion functions with a known frequency dependence, but with unknown diffusion-times that must be chosen based on the data to be transformed. Especially, accuracy of DEM is sensitive to the diffusion-time. In this study, we developed a method to determine the optimum range of diffusion-time values, minimizing the RMS error of the frequency-domain data approximated by the diffusion expansion. We confirmed that this method produces accurate results over a wider time range for a homogeneous half-space and two-layered model.